FlowMM is a novel generative model designed to predict and generate stable crystal structures, addressing the computational challenges in materials discovery. The model leverages Riemannian Flow Matching to handle the symmetries inherent in crystal structures, such as translation, rotation, and permutation, while maintaining periodic boundary conditions. By generalizing the Riemannian Flow Matching framework, FlowMM simplifies the problem of learning crystal structures compared to diffusion models, allowing for more efficient and flexible inference. The model is trained using Continuous Normalizing Flows (CNFs) with a finite time evolution, producing high-quality samples in terms of standard metrics and thermodynamic stability. FlowMM outperforms competing methods in both Crystal Structure Prediction (CSP) and De Novo Generation (DNG) tasks, achieving state-of-the-art performance on standard benchmarks. Additionally, it demonstrates significantly faster inference, reducing the number of integration steps required to find stable materials by a factor of 3 compared to previous open methods. FlowMM's effectiveness is validated through extensive experiments on realistic datasets and simplified unit tests, including the Materials Project (MP-20) and MPTS-52 datasets. The model's ability to generate stable and novel materials is further demonstrated by its competitive performance in stability metrics, such as the percent of generated materials that are stable, unique, and novel (S.U.N. Rate), and the average number of integration steps needed to generate a stable material (Cost). The paper concludes by highlighting the potential impact of FlowMM in advancing materials science, particularly in areas like energy storage, carbon capture, and microprocessing. The efficient and accurate generation of stable crystal structures using FlowMM could accelerate the discovery of novel materials with significant technological applications.FlowMM is a novel generative model designed to predict and generate stable crystal structures, addressing the computational challenges in materials discovery. The model leverages Riemannian Flow Matching to handle the symmetries inherent in crystal structures, such as translation, rotation, and permutation, while maintaining periodic boundary conditions. By generalizing the Riemannian Flow Matching framework, FlowMM simplifies the problem of learning crystal structures compared to diffusion models, allowing for more efficient and flexible inference. The model is trained using Continuous Normalizing Flows (CNFs) with a finite time evolution, producing high-quality samples in terms of standard metrics and thermodynamic stability. FlowMM outperforms competing methods in both Crystal Structure Prediction (CSP) and De Novo Generation (DNG) tasks, achieving state-of-the-art performance on standard benchmarks. Additionally, it demonstrates significantly faster inference, reducing the number of integration steps required to find stable materials by a factor of 3 compared to previous open methods. FlowMM's effectiveness is validated through extensive experiments on realistic datasets and simplified unit tests, including the Materials Project (MP-20) and MPTS-52 datasets. The model's ability to generate stable and novel materials is further demonstrated by its competitive performance in stability metrics, such as the percent of generated materials that are stable, unique, and novel (S.U.N. Rate), and the average number of integration steps needed to generate a stable material (Cost). The paper concludes by highlighting the potential impact of FlowMM in advancing materials science, particularly in areas like energy storage, carbon capture, and microprocessing. The efficient and accurate generation of stable crystal structures using FlowMM could accelerate the discovery of novel materials with significant technological applications.